A combination of political and personal pressures inside the White House and on Capitol Hill and the ineffectiveness of "quiet diplomacy" prompted President Reagan to make his first outspoken public criticism of South Africa, administration officials said yesterday.

These officials described Reagan's shift as one of tactics rather than policy but said the president's new willingness to speak out against South African segregation and repression could have policy consequences.

"We want results," an administration official said bluntly. "We want to see internal change."

Only a week ago, Assistant Secretary of State Chester A. Crocker insisted at a White House briefing that peaceful change was under way in South Africa. But Reagan, in a speech Monday marking International Human Rights Day, painted a different picture of what is going on in that nation.

"We feel a moral responsibility to speak out on this matter, to emphasize our concerns and our grief over the human and spiritual costs of apartheid in South Africa, to call upon the government . . . to reach out to its black majority by ending the forced removal of blacks from their communities and the detention without trial and lengthy imprisonment of black leaders," Reagan said.

Yesterday, in the wake of Reagan's speech, conservative Republican members of Congress, Democratic members of the congressional black caucus, South African Bishop Desmond M. Tutu and domestic protesters against apartheid all took credit for the president's new position.

Administration officials, acknowledging that all of those elements may have had an impact, said the intransigence of South Africa and the advocacies of moderate members of the White House staff played key roles in the president's decision.

White House deputy chief of staff Michael K. Deaver, chief of staff James A. Baker III and First Lady Nancy Reagan were described as having advocated outspoken presidential criticism of South Africa for its repressive policies.

Reagan considers himself a foe of bigotry and intolerance. Throughout his political career he has bridled whenever anyone suggested otherwise.

"The president was pursuing a policy that he believed was producing results," one official said. "He didn't like anyone saying that he was condoning segregation, which is not his position."

Members of the congressional black caucus hailed Reagan's denunciation of apartheid as a significant movement in U.S. policy and a victory for ongoing demonstrations against South African repression.

D.C. Del. Walter F. Fauntroy, an organizer of peaceful protests that began Nov. 21 in front of the South African Embassy here, said Reagan's statement "shows we are making progress inasmuch as he admits that quiet diplomacy does not always work."

The nonviolent protests, patterned after the civil rights demonstrations of the 1960s, were sparked by the early November arrests in South Africa of 16 black political opponents of the regime. It was these arrests and the protests to them that caused the Reagan administration to take a second look at "quiet diplomacy."

A senior administration official who briefed reporters at the White House on Monday, while insisting that Reagan administration policy was unchanged, acknowledged that there was "a built-in problem in our human rights policy" because its accomplishments couldn't be cited in public.

"There's no way around that except occasionally to veer away from private diplomatic efforts and go public," the official said. "It's a dangerous thing to do because if you push other governments too hard publicly . . . that may be counterproductive. But in the case of South Africa, I don't think we have any alternative . . . ."

The South African repression and the domestic protests triggered a letter on Dec. 4 by 35 Republican members of Congress, mostly young conservatives, to Ambassador Bernardus G. Fourie of South Africa.

They acted in the belief that it would be harder for Pretoria to write off protests from conservatives than from blacks and liberals demonstrating in the streets. They also expressed the determination that their generation of conservatives not be tarred with racism and warned of a blood bath in southwest Africa if South Africa fails to make progress toward racial justice.

"We have a longstanding concern over civil rights and we consider apartheid wrong," said Rep. Robert S. Walker (R-Penn.), who drafted the letter and was a civil rights demonstrator in Virginia and North Carolina as a college student. "We acknowledge the strategic value of South Africa but feared that our silence could indicate an acquiesence in apartheid. We feel strongly that progress needs to be made toward guaranteeing civil rights in South Africa and we would approve changes in U.S. policy, such as curtailment of new investment and diplomatic and economic sanctions, if there isn't."

"A small group of left-wing activists picketing in the streets doesn't matter," said Rep. Mickey Edwards (R-Okla.), one of the signers. "But when we speak out -- and the president does -- that matters."

They also expressed a strong feeling that racism is incompatible with conservative principles.

"We as conservatives have nothing in common with a government that denies basic rights to its citizens," Edwards said. "The essence of conservatism is the dignity of the individual. This is consistent with our rinciples."

"It is important that the next generation of conservative leadership send a signal to South Africa," said Rep. Vin Weber (R-Minn.). "If we are to become the majority party we have to change the perception of conservatives on civil rights. There is a consensus in the country on civil and human rights and we need to shuck the baggage of an ugly strain of American conservatism in the past, the baggage of racism."

Fauntroy and another member of the black caucus, Rep. John Conyers Jr. (D-Mich.), expressed appreciation of the conservatives' effort.

"Thanks to the president and that clumsy government in Pretoria, world opinion perceives that they've gone too far," Conyers said.

Several of the signers spoke of a racial "armageddon" if there's no progress in the matter.

"We can't hold back because of South Africa's strategic importance," Weber said. "We are heading toward the bloodiest race battle in the history of the world and if that happens our strategic interests are doomed."

Yesterday some administration officials expressed concern that Reagan's new outspokenness may make it marginally more difficult to reach a solution in Namibia. The United States is trying to prod South African forces to withdraw from Namibia, a black nation created by South Africa within its borders, in exchange for withdrawal of Cuban forces from Angola.

Officials said that this was a consideration in discussions with the president but that a Namibian solution "remains within our grasp." One official said, however, that this may not involve the complete withdrawal of Cuban forces.

As if to underscore the new toughness in U.S. policy toward South Africa, an official said he hoped that Reagan's speech would not harm a Namibian settlement, but added, "It's not the United States that's causing the problem, it's South Africa."